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Unformatted text preview: MMAE 350 D. Rempfer Problem Set VII Page 1 of 2 Due Date: November 20, 2006 1. We want to investigate the dynamics of the simple swinging pendulum (see picture), which is thought of as a point mass that is suspended on a rod of zero mass and length l , in a gravitational field with an acceleration of g . The angle between the vertical coordinate and the pendulum is denoted by . a. Use Newtons second law to derive the di ff erential equation that de scribes the change of the angle with time. b. Linearize the nonlinear di ff erential equation you have obtained above. (Hint: Use a Taylorseries expansion for the function on the righthand side of your di ff erential equation.) Q m l c. What is the exact solution of the linearized di ff erential equation, for ( t = 0) = 4 / 5, d /dt ( t = 0) = 0? d. Using Heuns predictorcorrector method, solve the exact di ff erential equation from part a. of this problem numerically, for the initial condition ( t = 0) = 4 / 5, d /dt ( t = 0) = 0, using g/ (2 ` ) = 1. Try to integrate over a time of t e = 4 , using step sizes h 1...
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This note was uploaded on 05/04/2008 for the course MMAE 350 taught by Professor Rempher during the Spring '05 term at Illinois Tech.
 Spring '05
 rempher

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